(at around 1h 24 mins) When Robert fixes up the puppets, Jester has the mace as his right hand, but near the end of the movie when the puppets thank Robert, he has a mace for his left hand instead.
(at around 59 mins) When Sgt. Russell shoots Jack Attack, she blows off the front of his box. In the next, there's no damage to the box.
(at around 1h 24 mins) After Pinhead gets his arm shot off, Sgt. Russell picks him up and hands his arm to Alex, the next shot shows her handing Alex the arm again.
(at around 12 mins) When the robberies come into the puppet garage, there's a close-up shot of Pinhead moving his head to the side, but directly after there's a scene of the burglars and Pinhead can be seen in the background with his head facing forward instead of the side.
(at around 35 mins) The part being examined under microscope by Robert Toulon and Alexandra Toulon is simply an electronic capacitor, not a camera.
(at around 8 mins) At the beginning of the movie when Toulon is making his introduction to the puppets, puppet strings are visible for nearly all of the puppets.